def ss_crystal_dogbone(x,experiments,y_data):
# x[0] = lnK_pm
# x[1] = lnK_mw
# x[2] = lnK_vw
# x[3] = lnD
# x[4] = phi
K_pm = np.exp(x[0])
#K_wm = np.exp(-x[1])
#K_vw = np.exp(x[2])
#K_vm = K_vw*K_wm
#D = np.exp(x[3])
#phi = x[4]
D = np.exp(x[1])
phi = x[2]
K_vw = 10.
K_wm = 0.0001
K_vm = K_vw*K_wm
uptake = []
for exp in experiments:
mass_dogbone = exp['mass_dogbone']
rho_c = exp['rho_c']
rho_a = exp['rho_a']
A = exp['A']
L = mass_dogbone/(rho_c+(rho_a-rho_c)*phi)/A
V = exp['V']
try:
moles_t = exp['moles_t']
except:
moles_t = exp['mass_t']/exp['MW_t']
c_in = moles_t/V
phi_L = exp['phi_L']
mass_surf = exp['mass_surf']
density_mic = exp['density_mic']
phi_M = (mass_surf/density_mic)/(V*phi_L)
K = K_pm/(phi_L*phi_M + phi_L*(1-phi_M)*K_wm + (1-phi_L)*K_vm)
nu = exp['nu']
t_data = exp['times']
# Run the diffusion code
time, uptake_piece, _ = crystal_dogbone(V, A, K, c_in, D, L, phi, nu, 200, times_to_save=t_data)
uptake += uptake_piece
return np.sum((np.array(uptake)-np.array(y_data))**2)
def uptake(lnK_mw=lnK_mw, lnK_vw=lnK_vw, lnK_pm=lnK_pm, lnD=lnD, phi=phi):
"""
Return variable uptake given experimental input parameters and fluctuating model parameters.
"""
# Convert stochastic variables into form more usable by diffusion code
K_pm = np.exp(lnK_pm)
K_wm = np.exp(-lnK_mw)
K_vw = np.exp(lnK_vw)
K_vm = K_vw*K_wm
D = np.exp(lnD)
# List of output data
uptake = []
for exp in experiments:
# Set parameters and run dogbone for each experiment. Note this means that computational expense increases
# as the number of experiments! If all parameters are identical except for the time, then use a single
# experiment with ```times``` equal to a list or numpy array of the times to report.
#
# Make sure not to read from experimental parameters when you should be using the stochastic variable!
mass_dogbone = exp['mass_dogbone']
rho_c = exp['rho_c']
rho_a = exp['rho_a']
A = exp['A']
L = mass_dogbone/(rho_c+(rho_a-rho_c)*phi)/A
V = exp['V']
try:
moles_t = exp['moles_t']
except:
moles_t = exp['mass_t']/exp['MW_t']
c_in = moles_t/V
phi_L = exp['phi_L']
mass_surf = exp['mass_surf']
density_mic = exp['density_mic']
phi_M = (mass_surf/density_mic)/(V*phi_L)
K = K_pm/(phi_L*phi_M + phi_L*(1-phi_M)*K_wm + (1-phi_L)*K_vm)
nu = exp['nu']
t_data = exp['times']
# Run the diffusion code
time, uptake_piece, _ = crystal_dogbone(V, A, K, c_in, D, L, phi, nu, 200, times_to_save=t_data)
# Note that order of data in uptake must be same as in y_data for comparison!
uptake += uptake_piece
return uptake
def fake_crystal_dogbone(experiments):
times = []
uptake = []
masses = []
for exp in experiments:
# Look for unknown params in exp since we're generating fake data
K_pm = exp['K_pm']
K_vw = exp['K_vw']
K_mw = exp['K_mw']
D = exp['D']
density_mic = exp['density_mic']
# Calculate params that permeate.crystal_dogbone wants, same as in pymc model below
K_wm = 1./K_mw
K_vm = K_vw/K_mw
mass_dogbone = exp['mass_dogbone']
phi = exp['phi']
nu = exp['nu']
rho_c = exp['rho_c']
rho_a = exp['rho_a']
A = exp['A']
L = mass_dogbone/(rho_c+(rho_a-rho_c)*phi)/A
V = exp['V']
moles_t = exp['moles_t']
c_in = moles_t/V
phi_L = exp['phi_L']
mass_surf = exp['mass_surf']
phi_M = (mass_surf/density_mic)/(V*phi_L)
K = K_pm/(phi_L*phi_M + phi_L*(1-phi_M)*K_wm + (1-phi_L)*K_vm)
t_data = exp['times']
# Run the diffusion code
time, uptake_piece, _, profile = crystal_dogbone(V, A, K, c_in, D, L, phi, nu, 200, times_to_save=t_data,\
save_profile_flag=True)
times += time
uptake += uptake_piece
masses += [mass_dogbone]*len(time)
# MAKE SOME NOISE
exp_sigma = exp['exp_sigma']
uptake = np.array(uptake) + np.random.normal(0.,exp_sigma,size=len(uptake))
return times, uptake, masses, profile